The union has consistently asked to have a third-party on the sideline to assess whether or not a player should stay out of a game. And the union thinks that in the case of San Francisco 49ers quarterback Alex Smith and Chicago Bears quarterback Jay Cutler -- both of whom kept playing after taking their respective shots to the head -- players were left on the field in situations when an independent doctor likely would've pulled them from the game.

One union source said that "the system right now is not working. We thought we'd resolve it after the Colt McCoy issue. Then, not only was nothing done, but issues continue with detection."

Asked to respond to the idea of a third-party neurologist, NFL spokesman Greg Aiello referenced a recent comment from Dr. Richard Ellenbogen, co-chair of the NFL's head, neck and spine committee.

"Independent experts on the sidelines would make the situation worse, unless they had a baseline exam on each player," Ellenbogen said. "No one knows the players as well as the athletic trainers, period. Having said that, some teams already have neurosurgeons on the sidelines. Having a doc show up just for a game takes away the all-important baseline exam and continuity of care. It would be like getting operated upon by a surgeon who did not see you pre-operatively. Is that safer than having someone who saw you beforehand? The baseline is all-important in making an assessment if a player is OK after a hit."